15 beats are heard in 5 seconds when a piano key and a tuning fork of slightly higher frequency (440 Hz) are struck at the same time. What is the frequency of the sound emitted by the piano key?

Fp=440 - 15/5 = 437Hz = Freq. of piano.

Brent, check your 3-28-11, 11:57am post
for solution to your Pre-cal prob.

Thanks.

To determine the frequency of the sound emitted by the piano key, we need to find the difference between the frequencies of the piano key and the tuning fork.

First, we need to understand the concept of beats. In acoustics, beats occur when two sound waves with slightly different frequencies interfere with each other. The interference produces a periodic variation in the sound intensity, resulting in a "wobbling" effect. The number of beats per second is equal to the difference in frequencies between the two sound sources.

In this case, the given information is that 15 beats are heard in 5 seconds. This means that the beats occur at a rate of 15/5 = 3 beats per second.

Next, we know that the tuning fork has a frequency of 440 Hz. Let's assume the frequency of the piano key is f.

The beat frequency is the difference between the two frequencies, which in this case is 440 Hz - f Hz.

Since the beat frequency is 3 beats per second, we can set up the equation:

440 Hz - f Hz = 3 beats/s

Now, we can solve for f:

f Hz = 440 Hz - 3 beats/s

To convert the beats/s to Hz, we can multiply by the frequency of one beat, which is 1 second per beat:

f Hz = 440 Hz - 3 beats/s * 1 s/beat

f Hz = 440 Hz - 3 Hz

f Hz = 437 Hz

Therefore, the frequency of the sound emitted by the piano key is 437 Hz.