Question

Traditional Indonesian music uses an ensemble called a gamelan that is based on tuned percussion instruments somewhat like gongs. In Bali, the gongs are often grouped in pairs that are slightly out of tune with each other. When both are played at once, the beat frequency lends a distinctive vibrating quality to the music. Suppose a pair of gongs are tuned to produce notes at 151 Hz and 155 Hz. How many beats are heard if the gongs are struck together and both ring for 2.5 s?

Short answer

There would be 10 beats in 2.5 seconds

Step-by-step solution

Write the given information 

The frequencies at which the pair of gongs produces notes

f₁= 151 Hz

f₂= 155Hz

Both the gongs ring for the time t = 2.5 sec

To determine the number of beats in 2.5 s 

The frequency of the beats produced by the pair of gongs is given by

$$\begin{gathered} f_b=|f_1-f_2| \\ {f}_b=|155-151|Hz \\ {f}_b=4Hz \end{gathered}$$

Thus, the frequency of the beat is 4Hz

Now, the number of beats in time t =2.5 s

$$\begin{gathered} n=f_{b}xt \\ n=4x2.5 \\ n=10 \end{gathered}$$

Thus, there would be 10 beats in 2.5 seconds