Wave motion: longitudinal and transverse waves, wave speed

If the initial tension on a stretched string is doubled, then the ratio of the initial and final speeds of a transverse wave along the string is :

Two cars moving in opposite directions approach each other with speed of 22 m/s and 16.5 m/s respectively. The driver of the first car blows a horn having a frequency 400 Hz. The frequency heard by the driver of the second car is [velocity of sound 340 m/s] :

A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of \(15\ ms^{-1}\). Then, the frequency of sound that the observer hears in the echo reflected from the cliff is : (Take velocity of sound in air \(= 330\ ms^{-1}\))

A uniform rope of length L and mass \(m_1\) hangs vertically from a rigid support. A block of mass \(m_2\) is attached to the free end of the rope. A transverse pulse of wavelength \(\lambda_1\) is produced at the lower end of the rope. The wavelength of the pulse when it reaches the top of the rope is \(\lambda_2\). The ratio \(\lambda_2/\lambda_1\) is :