Question

A couple of tuning forks produce 2 beats in the time interval of 0.4 sec. So, the beat frequency is:
A) 8 Hz
B) 5 Hz
C) 2 Hz
D) 10 Hz

Answer 1

Hint:Beat frequency is defined as the ratio of beats to that of the time interval. The beat is defined as the interference pattern of two sound waves of slightly different frequencies. The beat consists of constructive interference or destructive interference.

Formula used:The formula of the beat frequency is given by,
\[ \Rightarrow {\text{Beat frequency}} = \dfrac{{{\text{Number of beats}}}}{{{\text{time interval}}}}\]

Complete step by step answer:
To calculate the frequency, we will need a number of beats, which is given as two beats and the time interval given for those beats is 0.4 second.
The beat frequency is calculated by dividing the number of beats with the time interval.
The formula of the beat frequency is given by,
\[ \Rightarrow {\text{Beat frequency}} = \dfrac{{{\text{Number of beats}}}}{{{\text{time interval}}}}\]

Now, the number of beats is 2 and the time interval is 0.4 seconds. Putting the value in the expression, we get
Beat frequency, equals number of beats divided by the time interval.
Therefore, the beat frequency will become two by point zero, which gives the beat frequency as twenty by four.
\[ \Rightarrow {\text{Beat frequency = }}\dfrac{{{\text{Number of beats}}}}{{{\text{time interval}}}}\]
\[ \Rightarrow {\text{Beat frequency }} = \dfrac{2}{{0.4}}\]
\[ \Rightarrow Beat{\text{ }}frequency{\text{ }} = \dfrac{{20}}{4}\]
\[ \Rightarrow {\text{Beat frequency }} = 5Hz\]
On solving it further, we will get the beat frequency as five Hertz (5 Hz).

The beat frequency of the turning forks is five Hertz (5 Hz). Thus, option B is the correct answer.

Note:
-A beat is like a pattern, one after another. So, tuning forks, as indicated by their name, have two forks which are vibrating in a pattern one after another.
-The vibration in the forks causes beats which are accounted for in the form of frequency at every interval of time.
-The frequency is explained as the number of events taking place in a certain period of time. It is measured in Hertz.