For a certain organ pipe, the first three resonance frequencies are in the ratio of $$1:3:5$$ respectively. If the frequency of fifth harmonic is $$405 \mathrm{~Hz}$$ and the speed of sound in air is $$324 \mathrm{~ms}^{-1}$$ the length of the organ pipe is _________ $$\mathrm{m}$$.

The equation of wave is given by

$$\mathrm{Y}=10^{-2} \sin 2 \pi(160 t-0.5 x+\pi / 4)$$

where $$x$$ and $$Y$$ are in $$\mathrm{m}$$ and $$\mathrm{t}$$ in $$s$$. The speed of the wave is ________ $$\mathrm{km} ~\mathrm{h}^{-1}$$.

A transverse harmonic wave on a string is given by

$$y(x,t) = 5\sin (6t + 0.003x)$$

where x and y are in cm and t in sec. The wave velocity is _______________ ms$$^{-1}$$.

A guitar string of length 90 cm vibrates with a fundamental frequency of 120 Hz. The length of the string producing a fundamental frequency of 180 Hz will be _________ cm.