First slide

Standing waves

Question

Two wires of same material and of same length are stretched between two fixed supports. Wire,{ is thicker than wire B. If the initial tensions are same (T_A =T_B) and temperature increases

Moderate

A

both T_A and T_B decrease equally
B

T_A, decreases more than T_B
C

T_A decreases less than T_B
D

both T_A and T_B remain same as before

Solution

We know that Young's modulus of a material is given by
$Y = \frac{stress}{strain} = \frac{(F / A)}{(Δl / l)} = \frac{F . l}{A \cdot Δl} F = \frac{Y \cdot A \cdot Δl}{l} or T = \frac{Y \cdot A \cdot Δl}{l} Given that T_{A} = T_{B} Given that T_{A} = T_{B} A / issmallerinthickerwire (4) Now consider the effect of heating . The decrease in strain is same and hence the decrease in tension in thicker whe is more than thinner wire . Thus T_{A} decreases more than T_{B} .$

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