Electricity and Waves - AP Physics 1

This problem emphasizes the importance of being able to sift through a problem statement and pick out only the information you need to solve the problem. We are given four values, but only need two of them. If you are unable to sift through the problem effectively, you are likely to get bogged down by all the details and waste time performing unneeded calculations.

To find the speed of sound in the water, we only need one equation:

We are given the frequency of the sound and its wavelength in water. It is important to note that the frequency of a sound does not change as it enters a different medium; only the velocity and wavelength do.

Plugging in our values, we get:

If you got the answer 400 m/s, watch your units! You probably divided 340 m/s by 0.85 m, which gives you units of 1/s. That is a unit of frequency, not velocity.

In order to determine the velocity of a wave, we need to know the frequency and wavelength. From the problem statement, we know that a wave is created every 2 seconds. This is the period of the wave; therefore we can say that the frequency is:

Now we just need the wavelength. We are told that there are four full waves over a distance of 5 meters.

We can use the following formula to get the velocity:

Longitudinal waves transmit energy by compressing and rarefacting the medium in the same direction as they are traveling. Sounds waves are longitudinal waves and travel by compressing the air through which they travel, causing vibration.

Light, X-rays, and microwaves are all examples of electromagnetic waves; even if you cannot recall if they are longitudinal or transverse, they are all members of the same phenomenon and will have the same type of wave transmission. Transverse waves are generated by oscillation within a plane perpendicular to the direction of motion. Oscillating a rope is a transverse wave, as it is not compressing in the direction of motion.

First we need to solve for intensity , given by:

, where is power, is the distance from the source of the sound.

In our case, and , therefore

To solve for sound level , we do

, where is the intensity and is the threshold of hearing.

In this problem,

, and

Sound is a longitudinal, or compression wave. A region of slightly more compressed air is followed by a region of slightly less compressed air (called a rarefaction). When the compressed air is behind the balloon, it pushes it forward, and when it is in front of the balloon, it pushes it back. This only works if the frequency is low, because the waves are long enough so that the balloon can react to them.

Recall that the formula for sound level given in decibels is given by:

, where is the intensity and is the threshold of hearing.

Sound level is proportional to intensity by:

If the intensity is increased by a factor of , sound level would increase by a factor of

The speed of sound is fastest in the least compressible media of the lowest density. Sound does not propagate in a vacuum. Air and water are compressible media, so sound does not travel as fast in these as it does in glass, an incompressible medium. In general, the speed of sound is greatest in solids, and within each phase, faster as density decreases.

We need to know the speed of light, which is:

We can use this to calculate the wavelength of any electromagnetic wave if we know the frequency, using the equation:

If you're unsure of how to come about this equation, you should be able to derive it by looking at your units. Use our given values to solve for the wavelength:

Since the wave has a frequency of 30Hz, we know it completes 30 cycles every second. As its velocity is , we also know that in that second, the wave has moved 10m. Dividing the total distance, 10m, by the number of cycles, 30, we get the number of meters travelled in each cycle which is the wavelength:

Speed is frequency times wavelength. So the frequency must be speed divided by wavelength. In this case:

This makes sense as in one second, the wave will have travelled 15m. Each meter is 5 cycles, so over the distance the wave has travelled in one second, it has completed cycles.

A trigonometric equation given by the following formula

Here, is given in meters, is given in Hertz, is given in seconds, and is given in meters. The period is given by:

In our case:

Coulomb's law gives the relationship between the force of an electric field and the distance between two charges:

The strength of the force will be inversely proportional to the square of the distance between the charges.

When the distance between the charges is doubled, the total force will be divided by four (quartered).

Use Ohm's law.

Radio waves travel at the speed of light . The relationship between wavelength, frequency, and wave speed is

, where is the wavelength and is the frequency.

In our case,

.

Therefore,

Amplitude refers to the strength of a wave and has no relation to its frequency. Frequency would only affect the period and phase, but not the amplitude.

Remember the equation for the doppler effect for a moving observer:

Now, identify the given information:

(This is the speed of sound in air.)

When you are moving towards the concert, the plus sign is used. Therefore, the apparent frequency is

When you are moving away from the concert, the negative sign is used. Therefore, the apparent frequency is

We can use the following equation to solve this problem:

where

v = velocity of sound

f = frequency

= wavelength

Rearranging for wavelength, we get:

Plugging in our values, we get:

You do not need to have this equation memorized in order to solve this problem. A very useful skill in physics is being able to solve problems based solely off your units.

We need to have an answer with the units of meters. We are given units of m/s and 1/s. How can we go from these to meters? Simply divide the value with the units of m/s by the value with the units of 1/s. This gives you an answer with the units of meters. Once written out, this is the final equation written above. No need to spend extra time memorizing the equation!

We simply need to know the Doppler effect equation to solve this problem:

Since the observer (you) is not moving, we can rewrite the equation as:

The reason for using addition in the denominator is explained below.

We know all of our values, so we can simply solve for the perceived frequency:

For the Doppler effect equation, don't waste your time trying to memorize whether the signs should be . We have purposely made them the same to emphasize the following idea. Think about the situation practically. The police car is moving away from you. Therefore, we know that the percieved frequency is going to be less than the source. How do we make the frequency lower? We either lower the numerator or increase the denominator. Since we can only manipulate the denominator, we will use the + sign. Knowing this will also help you immediately eliminate all answers in which the frequency is increased.

This is a two-step problem. First, we need to calculate the percieved frequency that you here, and then convert that frequency into a wavelength.

For calculating percieved frequency, we need the Doppler equation:

Plugging in our values we get:

The reasoning for the signs used is explained below.

Now we need to conver that frequency to a wavelength using the equation:

If you don't know this equation, use your units to reason it out!

Plugging in our values, we get:

For the Doppler effect equation, don't waste your time trying to memorize whether the signs should be . We have purposely made them the same to emphasize the following idea. Think about the situation practically. You are moving away from the source of the sound. This will lower the percieved frequency. How do we lower the frequency? Make the numerator smaller. Therefore, we subtract your (the observer's) velocity. The source is moving toward you. This will increase the percieved frequency. How do we increase the frequency? Decrease the denominator. Therefore, we also subtract his (the source's) velocity.