Question

4.A guitar player is deliberately trying to produce beats by bending one string to make it almost match another unbent string’s pitch. If the unbent string’s frequency is 343 Hz and he wants to hear nine beats in 2 s, what pitch(es) could he bend the string to?

Answer 1

When two sound sources of the same amplitude and similar frequencies f₁ and f₂ are played at a time, beats are produced with a frequency given by:

$f_{beat}=|f_2-f_1|$

Since the guitar player wants to hear 9 beats in 2 seconds, then:

$f_{beat}=\frac{9}{2s}=4.5Hz$

Then, the pitches that can be used are those whose difference with respect to the frequency of 343Hz is 4.5Hz:

$\begin{gathered} f_2=f_1\pm f_{beat} \\ \\ \Rightarrow f_2=343Hz\pm4.5Hz \\ \\ \therefore f_{2,1}=347.5Hz \\ f_{2,2}=338.5Hz \end{gathered}$

Therefore, the pitches he could bend the string to, are 347.5Hz and 338.5Hz.