KCET · Physics · Waves and Sound
A metallic wire of \( 1 \mathrm{~m} \) length has a mass of \( 10 \times 10^{-3} \mathrm{~kg} \). If a tension of \( 100 \mathrm{~N} \) is applied to a wire, what is the speed of transverse wave ?
- A \( 100 \mathrm{~ms}^{-1} \)
- B \( 10 \mathrm{~ms}^{-1} \)
- C \( 200 \mathrm{~ms}^{-1} \)
- D \( 0.1 \mathrm{~ms}^{-1} \)
Answer & Solution
Correct Answer
(A) \( 100 \mathrm{~ms}^{-1} \)
Step-by-step Solution
Detailed explanation
Given, length of wire, \( I=1 \mathrm{~m} ; \) mass of wire, \( m=10 \times 10^{-3} \mathrm{~kg} \) tension, \( T=100 \mathrm{~N} \)
Speed of transverse wave, \( v=\sqrt{\frac{\text { Tension }}{\text { linear density }}} \)
Linear density
\(=\frac{\text { mass }}{\text { length }}=\frac{10 \times 10^{-3}}{1}=10 \times 10^{-3} \)
\(\Rightarrow v=\sqrt{\frac{100}{10 \times 10^{-3}}}=\sqrt{10^{4}}=100 \mathrm{~ms}^{-1}\)
Therefore, speed of transverse wave \( =100 \mathrm{~ms}^{-1} \)
Speed of transverse wave, \( v=\sqrt{\frac{\text { Tension }}{\text { linear density }}} \)
Linear density
\(=\frac{\text { mass }}{\text { length }}=\frac{10 \times 10^{-3}}{1}=10 \times 10^{-3} \)
\(\Rightarrow v=\sqrt{\frac{100}{10 \times 10^{-3}}}=\sqrt{10^{4}}=100 \mathrm{~ms}^{-1}\)
Therefore, speed of transverse wave \( =100 \mathrm{~ms}^{-1} \)
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