The constituent waves of a stationary wave have amplitude, frequency and velocity as \(8cm\), \(30Hz\) and \(180\frac{cm}{s}\) respectively. Write down the equation for stationary waves.
Ans: \(y=16Cos\frac{\pi x}{3}Sin(60\pi t)\).
A wire is stretched between two rigid supports vibrates in its fundamental mode with a frequency of \(45Hz\).The mass of the wire is \(\left(3.5\times10^{-2}\right)Kg\) and its linear mass density is \(\left(4\times10^{-2}\right)\frac{kg}{m^{3}}\). What is the speed of transverse wave on string and tension in string?
Ans: \(v=78.75\frac{m}{s}\) and \(T=248N\).
Find: the frequency of the note emitted by string of length \(10\sqrt{10}cm\) under the tension \(3.14kg\). Radius of string is \(0.5mm\) and density is \(9.8\frac{g}{cm^{3}}\).
Ans: \(\nu=100Hz\).
A \(3.6g\) string of a sonometer is \(64cm\) long. What should be the tension in the string in order that it may vibrate in \(2\) segments with a frequency of \(256Hz\).
Ans: \(T=150N\).
A string vibrates with a frequency \(200Hz\). Its length is doubled and its tension is altered until it began to vibrate with a frequency of \(300Hz\) . Calculate: the ratio of new tension to the original tension.
Ans: \(\frac{T_{New}}{T_{Original}}=9\).
The length of a sonometer wire is \(0.75m\) and density is \(\left(9\times10^{3}\right)\frac{kg}{m^{3}}\). It can bear a stress of \(\left(8.1\times10^{8}\right)\frac{N}{m^{2}}\) with out exceeding the elastic limit. What is the fundamental frequency that can be produced in the wire?
Ans: \(\nu=200Hz\).
A wire of density \(9\frac{g}{c.c}\) is stretched between two clamps \(100cm\) apart Which is subjected to an extension of \(0.05cm\). What is the lowest frequency of transverse vibration in the string? Given: \(Y=\left(9\times10^{10}\right)\frac{N}{m^{2}}\).
Ans: \(\nu=35.4Hz\).
The length of a wire between two ends of a sonometer is \(126cm\). Where should the two bridges be placed so that the fundamental frequencies of three segments are in the ration of \(1:3:13\)?
Ans: at \(90cm\) and \(120cm\) from one end.
A wire having a linear mass density of \(\left(5.0\times10^{-3}\right)\frac{kg}{m}\) is stretched between two rigid supports with a tension of \(450N\). The wire resonates at a frequency of \(420Hz\). the next higher frequency at which wire resonates is \(490Hz\). find: the length of the wire.
Ans: \(L=2.14m\).
The two parts of a sonometer wire is divided by a movable knife edge differ by \(2mm\) and produces \(1\) beat per second when sounded together. Find: their frequencies if the whole length of wire is \(1m\).
Ans: \(\nu_{1}=249.5Hz\) and \(\nu_{2}=250.5Hz\).
A stone hangs in air from one end of a wire which is stretched over a sonometer. The wire is in unison with a certain tuning fork when the bridges of sonometer are \(45cm\) apart. Now the stone hangs immersed in water at \(4^{o}C\) and the distance between the bridges has to be altered by \(9cm\) to re-establish unison of the wire with the same tuning fork. Calculate: The density of the stone.
Ans: \(\rho=2.8\frac{gm}{cm^{3}}\).
In Melde’s experiment, a string vibrates in \(3\) loops when mass of \(8g\) placed in the pan. What mass must be placed in the pan so that the string vibrates in \(5\) loops?
