A standing wave exists in a string of length $150\ cm$ , which is fixed at both ends with rigid supports . The displacement amplitude of a point at a distance of $10\ cm$ from one of the ends is $5\sqrt 3\ mm$ . The nearest distance between the two points, within the same loop and havin displacment amplitude equal to $5\sqrt 3\  mm$ is $10\ cm$ . Find the maximum displacement amplitude of the particles in the string …. $mm$

The tension of a stretched string is increased by $69\%$. In order to keep its frequency of vibration constant, its length must be increased by ….. $\%$

A certain string will resonant to several frequencies, the lowest of which is $200 \,cps$. What are the next three higher frequencies to which it resonants?

A string under a tension of $129.6\,\, N$ produces $10\,\, beats /sec$  when it is vibrated along with a tuning fork. When the tension is the string is increased to $160\,\, N,$ it sounds in unison with same tuning fork. calculate fundamental freq. of tuning fork …. $Hz$

A hollow pipe of length $0.8 \mathrm{~m}$ is closed at one end. At its open end a $0.5 \mathrm{~m}$ long uniform string is vibrating in its second harmonic and it resonates with the fundamental frequency of the pipe. If the tension in the wire is $50 \mathrm{~N}$ and the speed of sound is $320 \mathrm{~ms}^{-1}$, the mass of the string is