MHT CET · Physics · Waves and Sound

Beats are produced by two waves given by \(y_{1}=a \sin 2000 \pi t\) and \(y_{2}=a \sin 2008 \pi t\). The
number of beats heard per second is

A zero
B one
C four
D eight

Verified Solution

Answer & Solution

Correct Answer

(C) four

Step-by-step Solution

Detailed explanation

Number of beats per second
\(=n_{1} \sim n_{2}\)
\(\omega_{1}=2000 \pi=2 \pi n_{1}\)
\(
\begin{array}{lc}
\Rightarrow & n_{1}=1000 \\
\text { and } & \omega_{2}=2008 \pi=2 \pi n_{2} \\
\Rightarrow & n_{2}=1004
\end{array}
\)
Number of beats heard per second
\(
=1004-1000=4
\)

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

Same subject

Explore more questions on app

From MHT CET

Explore more questions on app

Beats are produced by two waves given by \(y_{1}=a \sin 2000 \pi t\) and \(y_{2}=a \sin 2008 \pi t\). Thenumber of beats heard per second is

Step-by-step Solution

Beats are produced by two waves given by \(y_{1}=a \sin 2000 \pi t\) and \(y_{2}=a \sin 2008 \pi t\). The
number of beats heard per second is