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?

You mean 437 in your final answer. 440-3=437 not 337

440-f=15

Number of beats heard per second = 15/5 = 3 beats/sec. We know number of beats heard per second = difference in frequency of the two sound waves. So 3 = 440 - fp, where fp is the frequency of the piano key which is slightly lower than 440 Hz. Solving for fp, we get fp = 337 Hz.

337

To find the frequency of the sound emitted by the piano key, we can use the concept of beats. When two sound waves of slightly different frequencies overlap, they create a "beating" or pulsating sound. The number of beats per second is proportional to the difference in frequency between the two waves.

In this case, we know that there are 15 beats in 5 seconds. To find the frequency of the piano key, we need to determine the difference in frequency between the piano key and the tuning fork.

Let's start by calculating the beat frequency. We know that the number of beats per second is equal to the difference in frequency divided by the time in seconds:

Number of beats per second = Difference in frequency / Time

In this case, the number of beats is 15 and the time is 5 seconds. Let's substitute these values:

15 beats/second = Difference in frequency / 5 seconds

We want to find the difference in frequency, so we can rearrange the equation:

Difference in frequency = 15 beats/second * 5 seconds
Difference in frequency = 75 Hz

Now that we know the difference in frequency, we can calculate the frequency of the piano key. The tuning fork has a frequency of 440 Hz, so the frequency of the piano key can be determined by adding or subtracting the difference in frequency from the tuning fork's frequency:

Frequency of piano key = 440 Hz +/- 75 Hz

There are two possible frequencies for the piano key:

Frequency 1: 440 Hz + 75 Hz = 515 Hz
Frequency 2: 440 Hz - 75 Hz = 365 Hz

Therefore, the frequency of the sound emitted by the piano key can be either 515 Hz or 365 Hz, depending on whether the difference in frequency causes the sound to be higher or lower than the tuning fork's frequency.