Frequency and Intensity Level of Sound Waves

[craig.16]

(b) The frequency of sound waves received by a detector when both source and detector move
relative to the air is:
f=f₀[u(+ or -)v_d/u(+ or -)v_s] . Two trains are approaching each other at a level
crossing and blow their whistles at a frequency of 500 Hz. Train 1 is traveling at 20% of the
speed of sound while train 2 is traveling at 5% of the speed of sound.
i) What is the perceived frequency of the whistle sounded by train 1 when heard by an
observer on train 2? [3]
ii) The sound intensity levels of the two trains are 88 dB and 85 dB respectively. What is
the combined sound intensity level of the two trains?

Homework Equations

f=f₀[u(+ or -)v_d/u(+ or -)v_s]

The Attempt at a Solution

For part (i):
I took u=344ms^-1 (speed of sound)
v_d=-0.05c (going in opposite direction of train 1)
v_s=0.2c
since it is going towards train 1 i made the sign on the top of the equation a plus and since the source is moving towards the detector on train 2 I made the bottom sign a minus. Using this I received and answer of f=125Hz for the perceived frequency. Is this correct?

For the second part do I simply add the intensity levels together and divide by two to get an average since I am unsure on this part. Thanks in advance.

 

[anathema]

I would like to clarify and add some additional information about the concept of the perceived frequency of sound waves.

First, the equation provided in the forum post is known as the Doppler effect equation and is used to calculate the perceived frequency of a sound wave when there is relative motion between the source and the detector. It takes into account the speed of sound (u), the velocity of the source (vs), and the velocity of the detector (vd). The plus or minus signs indicate whether the source and detector are moving towards or away from each other.

Now, to answer the first part of the question, we can use the given information to calculate the perceived frequency of the whistle sounded by train 1 when heard by an observer on train 2. Using the Doppler effect equation and the given values, we get:

f = 500 Hz [344 m/s + (-0.05)(344 m/s)] / [344 m/s + (-0.2)(344 m/s)] = 125 Hz

So, your answer of 125 Hz is correct.

For the second part of the question, we need to understand the concept of sound intensity levels. Sound intensity level is a measure of the sound energy per unit area and is measured in decibels (dB). The equation for sound intensity level is:

IL = 10 log (I/I0)

Where I is the sound intensity and I0 is the reference intensity, which is usually taken as 10^-12 W/m^2. In this case, we are given the sound intensity levels of the two trains, which are 88 dB and 85 dB respectively. To calculate the combined sound intensity level, we use the following equation:

IL = 10 log (I1/I0 + I2/I0)

Where I1 and I2 are the sound intensities of the two trains. Plugging in the given values, we get:

IL = 10 log (10^8/10^-12 + 10^5/10^-12) = 86.7 dB

So, the combined sound intensity level of the two trains is 86.7 dB.

In conclusion, as a scientist, it is important to understand the concepts and equations that govern the perceived frequency and sound intensity levels of sound waves. It is also important to carefully consider the given information and use the correct equations to arrive at the correct answers.