Chapter 10.2, Problem 13R

To determine

Number of wavelengths passing in one minute for each musical note and give the relationship between frequency and number of wavelengths passing in one minute.

Answer to Problem 13R

The required volume is $\boxed{v=64{\text{ cm}}^3}$ .

Explanation of Solution

Given:

The table of frequency for different musical notes is shown below,

  

Introduction:

In musical notes, the frequency is normally related to the pitch. Pitch may be counted as frequency, but pitch is not a purely objective physical property; it is rather a subjective property of sound.

The relationship of the speed of sound, its frequency, and wavelength is the same as for all waves: v = fλ, where vis the speed of sound, f is its frequency, and λ is its wavelength. 

Formula used:

The expression for wavelength of a note is,

  $\lambda =v/f$  ...... (1)

Here, λ is the wavelength of the note, v is the velocity of sound and f is the frequency.

Equation (1) is the relation between frequency and wavelength.

Calculation:

Substitute 330 m/s for v and 262 Hz, 294Hz, 330 Hz, 349 Hz, 392 Hz, 440 Hz, 494 Hz and 523 Hz for the frequencies f in equation (1)

Frequencies (Hz)	Wavelengths (meter)
262	1.259
294	1.12
330	1
349	0.945
392	0.841
440	0.75
494	0.668
523	0.63

Conclusion:

Hence, the required wavelengths obtained are given in the above table.