The length of the wire shown in figure (15-E8) between the pulley is 15 m and its mass is 120 g. Find the frequency of vibration with which the wire vibrates in two loops leaving the middle point of the wire between the pulleys at rest.

A piano wire weighing 600 g and having a length of 900 cm emits a fundamental frequency corresponding to the “Middle C” (ν = 26163 Hz). Find the tension in the wire.

A sonometer wire having a length of 150 m between the bridges vibrates in its second harmonic in resonance with t tuning fork of frequency 256 Hz. What is the speed of the transverse wave on the wire?

A one-metre long stretched string having a mass of 40 g is attached to a tuning fork. The fork vibrates at 128 Hz in a direction perpendicular to the string. What should be the tension in the string if it is to vibrate in four loops?

A wire, fixed at both ends is seen to vibrate at a resonant frequency of 240 Hz and also at 320 Hz. (A) What could be the maximum value of the fundamental frequency? (B) If transverse waves can travel on this string at a speed of 40 m s⁻¹, what is its length?