Two speakers, A and B, are emitting identical, synchronized (in-phase) sound waves at 240kHz. A person standing a point C hears a relatively loud sound. She then starts walking towards point D, and notices the sound gets quieter, reaching a minimum when she arrives at D. The distance from speaker A to D is 3.10m. The distance from speaker B to D is 2.40m.
a) From the information given above,what is the wavelength of the sound?
b) From the information given above, what is the speed of the sound?
To find the wavelength of the sound, we can use the formula:
wavelength = speed of sound / frequency
To find the speed of sound, we need to first find the frequency. Given that speaker A and B are emitting identical, synchronized sound waves at 240 kHz, the frequency is 240 kHz.
So, the frequency (f) = 240 kHz = 240,000 Hz.
Now, let's find the wavelength:
a) From the information given above, what is the wavelength of the sound?
Step 1: Find the distance traveled from point C to D by the person.
The distance from speaker A to D is 3.10m.
The distance from speaker B to D is 2.40m.
Step 2: Calculate the path difference between the two speakers (Δx).
Δx = Distance from A to D - Distance from B to D
Δx = 3.10m - 2.40m
Δx = 0.70m
Step 3: Calculate the number of wavelengths (n) in the path difference.
n = Δx / wavelength
Since the path difference is equal to an integer multiple of the wavelength for constructive interference, we have n = 1.
Step 4: Calculate the wavelength.
wavelength = Δx / n
wavelength = 0.70m / 1
wavelength = 0.70m
Therefore, the wavelength of the sound is 0.70m.
b) From the information given above, what is the speed of the sound?
To find the speed of sound, we can rearrange the formula:
speed of sound = wavelength * frequency
Given:
wavelength = 0.70m
frequency = 240 kHz = 240,000 Hz
speed of sound = 0.70m * 240,000 Hz
speed of sound = 168,000 m/s
Therefore, the speed of sound is 168,000 m/s.