Question

Standing waves on a 1.0-m-long string that is fixed at both ends are seen at successive frequencies of 36 Hz and 48 Hz. a. What are the fundamental frequency and the wave speed? b. Draw the standing-wave pattern when the string oscillates at 48 Hz.

Short answer

a) 12Hz, 24m/s

b) Standing wave pattern will be a fourth harmonic over a length of 1m.

Step-by-step solution

Given parameters

Length of string: 1m

Successive frequencies: 36Hz, 48Hz

Part a:

Fundamental frequency = 48Hz - 36Hz = 12Hz

Solving for wave speed:

$$\begin{gathered} f_1=\frac{\nu }{2L} \\ \nu =f_1\times 2L \\ \nu =12\times 2 \\ \nu =24m/s \end{gathered}$$

Part b:

When string oscillates at 48Hz, It will be fourth harmonic.