Finding the wavelength and frequency

[sonutulsiani]

Homework Statement

A sound source is moving at 80 m/s toward a stationary listener that is standing in still air. The source emits sound at a frequency of 200Hz. Assume that the sound travels at still air at 343 m/s.

1. The wavelength of the sound in the region between the source and the listener is

A. 2.12 m
B. 1.72 m
C. 1.32 m
D. 1.82 m


2. The frequency heard by the listener using the above wavelength is

A. 261 Hz
B. 320 Hz
C. 199 Hz
D. 162 Hz

A sound source is moving at 80 m/s from a stationary listener that is standing in still air. The source emits sound at frequency of 200 Hz that travels in still air at 343 m/s.


3. The wavelength of the sound in the region between the source and the listener is

A. 2.12 m
B. 1.72 m
C. 1.32 m
D. 1.82 m


4. The frequency heard by the listener

A. 260 Hz
B. 320 Hz
C. 199 Hz
D. 162 Hz

Homework Equations

The Attempt at a Solution

So the first one I got it as 343-80=263 m/s Then wavelength = velocity / frequency = 263/200 = 1.32

2. Frequency = velocity/wavelength = 343/1.32 = 261 HZ

3. 343+80=423 m/s wavelength= 423/200 = 2.12

4. Frequency = 343/2.12 = 162 Hz

Are these correct?

 

[anathema]

Your calculations and answers are mostly correct, but here are some additional explanations and corrections:

1. The first question asks for the wavelength "in the region between the source and the listener." This means that we need to consider the relative motion of the source and the listener. In this case, the source is moving towards the listener, so the wavelength will be compressed. This effect is known as the Doppler effect. The correct calculation would be wavelength = velocity / (frequency * (velocity of sound - relative velocity)). So in this case, it would be 343 / (200 * (343 - 80)) = 1.72 m. Therefore, the correct answer is B.

2. Your answer for the second question is correct, but you can also use the same formula as in question 1 to get the answer. It would be frequency = velocity / (wavelength * (velocity of sound - relative velocity)) = 343 / (1.72 * (343 - 80)) = 261 Hz.

3. Your calculation and answer for question 3 are correct. However, you could also use the same formula as in question 1 to get the answer. It would be wavelength = velocity / (frequency * (velocity of sound + relative velocity)) = 423 / (200 * (343 + 80)) = 2.12 m. Therefore, the correct answer is A.

4. Your answer for the fourth question is incorrect. To find the frequency heard by the listener, we need to use the same formula as in question 3, but with the new wavelength calculated in question 3. It would be frequency = velocity / (wavelength * (velocity of sound + relative velocity)) = 343 / (2.12 * (343 + 80)) = 162 Hz. Therefore, the correct answer is D.

 

[kerimek]

I would like to clarify a few things about the problem and your solutions. First, it is important to note that the given frequency of 200 Hz is the frequency emitted by the sound source, not the frequency heard by the listener. The frequency heard by the listener will be different due to the Doppler effect, which is caused by the relative motion between the source and the listener.

For the first question, you correctly calculated the wavelength using the formula wavelength = velocity/frequency. However, the answer should be in meters, not m/s. So the correct answer is 1.72 m.

For the second question, you used the wrong formula to calculate the frequency heard by the listener. The correct formula is frequency = (velocity + observer's velocity)/(wavelength + source's velocity). Plugging in the values, we get frequency = (343+80)/(1.72+80) = 3.59 Hz. This is the frequency heard by the listener.

For the third question, you correctly calculated the wavelength using the formula wavelength = velocity/frequency. However, the velocity you should use is the sum of the source's and observer's velocities, which is 343+80 = 423 m/s. So the correct answer is 2.12 m.

For the fourth question, you used the wrong formula again. The correct formula is frequency = (velocity + observer's velocity)/(wavelength + source's velocity). Plugging in the values, we get frequency = (343+80)/(2.12+80) = 3.56 Hz. This is the frequency heard by the listener.

In conclusion, it is important to carefully read and understand the problem before attempting to solve it. Also, make sure to use the correct formulas and units in your calculations.