Q20DQ - University Physics with Modern Physics

Question

Violins are short instruments, while cellos and basses are long. In terms of the frequency of the waves they produce, explain why this is so.

Step-by-Step Solution

Answer

The wavelength of short instruments is small and the wavelength of long instruments is large. Therefore, the frequency of short instruments is high while for long instruments the frequency is low. 

STEP 1: Concept of frequency of the string.

The frequency of a string is directly proportional to the square root of its tension.

The frequency of the string is given by 

$\mathrm{f}=\frac{1}{2\mathrm{L}}\sqrt{\frac{\mathrm{T}}{\mathrm{\mu }}}$                                                                                                              ….. (1)

Here, L is the length of the string, T is the tension, $\mathrm{\mu }$ is the linear mass density.

Step 2 The frequency is depends upon three factors of instruments :

The length of strings of instruments. Tension in the strings. And mass per unit length of the instrument. From equation (1) it can be concluded that the frequency of vibrating instruments is inversely proportional to its length of string, square root of mass per unit length of string, and directly proportional to the square root of the tension in the string. If there is any change in any of these factor frequencies gets changed.

 

Therefore, the wavelength of short instruments is small and the wavelength of long instruments is large. Therefore, the frequency of short instruments is high while for long instruments the frequency is low.