Two timpani (tunable drums)are played at the same time.One is correctly tuned so that when it is struck,sound is produced that has a wavelength of 2.20 m.The second produces sound with a wavelength of 2.10 m.If the speed of sound is 343 m/s,what beat frequency is heard?
A)7 beats/s
B)9 beats/s
C)11 beats/s
D)13 beats/s
E)15 beats/s

Question

Quizplus · Accepted Answer

The beat frequency is calculated by finding the difference between the frequencies of the two sounds. First, calculate the frequencies of both sounds using the formula $f = v/\lambda$, where $v$ is the speed of sound and $\lambda$ is the wavelength. For the first timpani, $f_1 = 343 \, \text{m/s} / 2.20 \, \text{m} = 155.91 \, \text{Hz}$, and for the second, $f_2 = 343 \, \text{m/s} / 2.10 \, \text{m} = 163.33 \, \text{Hz}$. The beat frequency is the absolute difference between these two frequencies: $|f_2 - f_1| = |163.33 \, \text{Hz} - 155.91 \, \text{Hz}| = 7.42 \, \text{Hz}$, which rounds to approximately 7 beats/s.

Two Timpani (Tunable Drums)are Played at the Same Time