A string of mass 2.5 kg is under tension of 200 N . The length of the stretched string is 20.0 m . If the transverse jerk is struck at one end of the string, the disturbance will reach the other end in

A train whistling at constant frequency is moving towards a station at a constant speed $v$. The train goes past a stationary observer on the station. The frequency $n^{\prime}$ of the sound as heard by the observer is plotted as a function of time $t$ (figure). Identify the expected curve.

$$\begin{aligned} &\text { A transverse harmonic wave on a string is described by }\\ &y(x, t)=3.0 \sin \left(36 t+0.018 x+\frac{\pi}{4}\right) \end{aligned}$$

where $x$ and $y$ are in cm and $t$ is in sec. The positive direction of $x$ is from left to right.

The displacement of a string is given by

$$y(x, t)=0.06 \sin \left(\frac{2 \pi x}{3}\right) \cos (120 \pi t)$$

where $x$ and $y$ are in metre and $t$ in second. The length of the string is 1.5 m and its mass is $3.0 \times 10^{-2} \mathrm{~kg}$.

Speed of sound wave in a fluid depends upon