Two wavelengths, find time between successive beats

In summary, two pianos sound the same note simultaneously, but are out of tune. The speed of sound is 348 m/s and piano A has a wavelength of 0.765 m while piano B has a wavelength of 0.772 m. The frequencies of A and B are 454.9 and 450.7, respectively. To find the time between successive beats, we use the formula T = 1/Δf, where Δf is the difference in frequency. So, the time between beats would be 2 seconds if the difference in frequency is 1/2 hz.
  • #1
phys62
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Two pianos each sound the same note simultaneously, but they are both out of tune. On a day when the speed of sound is 348 m/s, piano A produces a wavelength of 0.765 m, while piano B produces a wavelength of 0.772 m. How much time separates successive beats?


So I know:
v=348 m/s
wavelength of A=0.765 m
wavelength of B=0.772 m
f=v/wavelength

so I was able to find the frequency of A=454.9 and frequency of B=450.7
I'm just not really sure what I should be doing... seems like it should be just a one or two step problem.. :/
 
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  • #2
OK what is the difference in frequency?

Isn't a beat going to be counted when ever their maxima coincide? So say the difference between 2 tones Δf is 1/2 hz, then won't the time T between maxima be 1/Δf = 2 ?
 
  • #3
Yes, you're right! Thanks so much!
 

FAQ: Two wavelengths, find time between successive beats

1. What are two wavelengths and how are they related?

Two wavelengths refer to the distance between two successive peaks or troughs in a wave. They are related by the frequency of the wave, which is the number of complete oscillations per unit time. The shorter the wavelength, the higher the frequency and vice versa.

2. How does the time between successive beats relate to two wavelengths?

The time between successive beats is directly related to the wavelength and frequency of a wave. The shorter the wavelength, the shorter the time between successive beats and the higher the frequency. The longer the wavelength, the longer the time between successive beats and the lower the frequency.

3. Can the time between successive beats be calculated from two given wavelengths?

Yes, the time between successive beats can be calculated by dividing the difference between the two wavelengths by the speed of the wave. This can be represented by the formula: time = (wavelength2 - wavelength1) / speed

4. How does the speed of the wave affect the time between successive beats?

The speed of the wave directly affects the time between successive beats. The faster the wave travels, the shorter the time between successive beats and vice versa. This is because the speed of the wave is directly proportional to the frequency and inversely proportional to the wavelength.

5. What factors can affect the time between successive beats of a wave?

The time between successive beats of a wave can be affected by the speed of the wave, the wavelength, and the frequency. Additionally, factors such as medium (solid, liquid, or gas) and temperature can also affect the speed of the wave and consequently, the time between successive beats.

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