Question

The frequency of a man’s voice is 300Hz and its wavelength is 1 meter. If the wavelength of a child’s voice is 1.5m, then the frequency of the child’s voice is:
A). 200Hz
B). 150Hz
C). 100Hz
D). 350Hz

Answer 1

Hint: With the help of the velocity of the sound expression
$\text{ Velocity of sound }= \left( \text{wavelength} \right) \times \left( \text{frequency} \right) $
  $v = \lambda \times f $

Complete step by step solution:
With the help of the above expression we calculate the frequency of the child.
$v = \lambda \times f$
v is the velocity of the sound
$\lambda $ is the wavelength
f is the frequency
This expression is the same for both the man’s voice and the child’s voice.
For man,
We have the given value of the frequency of the man and the wavelength to find the velocity of the sound.
${v_m} = {\lambda _m} \times {f_m}$ --- (1)
Here, wavelength of the man is 1m,
Frequency of the man is 300Hz
So, we put the value in equation (1)
$
  {v_m} = 1 \times 300 \\
   \Rightarrow {v_m} = 300m/s \\
 $
Now, we calculate the frequency of the child’s voice
${v_c} = {\lambda _c} \times {f_c}$ --- (2)
Here, we have the value of wavelength of the child is 1.5m,
The velocity of the sound remains the same in man’s voice and child’s voice.
${v_c} = {v_m} = 300m/s$
So, we put the value in equation (2)
$
  300 = {\text{1}}{\text{.5}} \times {f_c} \\
   \Rightarrow {f_c} = \dfrac{{300}}{{1.5}} \\
   \Rightarrow {f_c} = 200Hz \\
 $
So, the frequency of the child is 200Hz.
So, the option (A) is correct.

Note: The average frequency of a male’s voice is 125Hz.
The average frequency of a female’s voice is 200Hz.
The average frequency of a child’s voice is 300Hz.
The low frequencies sounds are harmful. The person is able to detect the sound range of 20 to 20000Hz. Under the frequency of the 20Hz it can also affect the ear.
The most dangerous frequency is the median alpha-rhythm frequencies that are of 7 Hz.