Question

A sound wave of frequency 330 Hz is incident normally at a reflected wall then minimum distance from the wall at which particles vibrate very much :- (V$_{sound}$ = 330 m/s).
A. 0.25m
B. 0.125m
C. 1m
D. 0.5m

Answer 1

Hint: To solve this question, firstly we have to understand the concept of the sound wave frequency, why and how it is incident normally at the reflected wall. We will be using the values which are given in the questions i.e. frequency and Vsound. By using the correct formula we will find out the right answer.

Complete step by step answer:
The sensation which is felt by our ears is called sound and it travels in the form of a wave. In our everyday life we hear several sounds. In a medium the vibratory disturbance is known as a wave. A wave carries energy from one place to another without coming into a direct contact between two ends or place.
A sound wave is described by its:
1. Frequency
2. Amplitude
3. Speed or velocity
4. Wavelength
5. Time period
There are two kinds of waves:
A. Longitudinal waves
B. Transverse waves
Sound waves are the longitudinal waves.
The SI unit of frequency in the Hertz symbol is Hz. Heinrich Rudolf Hertz named this. It means one cycle per second. 1 Hertz frequency is equal to the period of 1 second.
For example: 30Hz to cycles per second= 30
Inverse of frequency is period.
Given,
$
 Frequency = 330Hz \\
  Velocity = 330m/s \\
$
Formula used: $\lambda = \dfrac{v}{f}$
By treating the second waves as standing pressure waves, we will get
$
  \lambda = \dfrac{v}{f} = \dfrac{{330m/s}}{{330Hz}} \\
   = 1m \\
$
Hence, the distance which is minimum from the wall at which a particle vibrates very much is equal to the distance which is minimum from the wall and the pressure is zero.
With distance the pressure of the wave is represented.
Now, the distance required is
$
  \dfrac{\lambda }{4} \\
  i.e. \dfrac{1}{4}m = 0.25m \\
$

So, the correct answer is “Option A”.

Note: The formula for wave equation is $v = f \times \lambda $ is applied to all the waves like + transverse waves (water waves), longitudinal waves (sound waves), and the electromagnetic waves (light and radio waves). Hz is the S.I. unit of frequency and it is written and pronounced as Hertz. A body which vibrates 1 wave per second has a frequency of 1 Hz. Frequency of waves and the frequency of the vibrating body is the same.