Question

Two vibrating tuning forks produce waves given $y_1 = 4 \sin 500 \pi t$ and $y_2 = 2 \sin 506 \,\pi t.$ Number of beats produced per minute is

• A. 360
• B. 180
• C. 60
• D. 3

Answer 1

The Correct Option is B

To solve the problem of determining the number of beats produced per minute by the two tuning forks, we first need to understand the concept of beats in physics. Beats occur when two sound waves of slightly different frequencies interfere, leading to variations in sound intensity at regular intervals.

1. The frequencies of the two waves are derived from their equations:

   • First wave: y_1 = 4 \sin 500\pi t, giving a frequency f_1 = \frac{500}{2} = 250 \, \text{Hz}.
   • Second wave: y_2 = 2 \sin 506\pi t, giving a frequency f_2 = \frac{506}{2} = 253 \, \text{Hz}.

2. The beat frequency, which is the difference between the two frequencies, is calculated as:

   f_{\text{beat}} = \left| f_1 - f_2 \right| = \left| 250 \, \text{Hz} - 253 \, \text{Hz} \right| = 3 \, \text{Hz}

3. The number of beats per minute can be found by multiplying the beat frequency by 60 (since there are 60 seconds in a minute):

   \text{Beats per minute} = f_{\text{beat}} \times 60 = 3 \, \text{Hz} \times 60 \, \text{s/min} = 180 \, \text{beats/min}

Therefore, the number of beats produced per minute by the two tuning forks is 180.