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question_answer1) The equation of a standing wave produced on a string fixed at both the ends is ? \[y=(0.4)\sin \left[ (0.314\,c{{m}^{-1}})x \right]\cos \left[ (600\,\pi \,{{s}^{-1}})t \right]\] What would be the smallest length of the string (in cm)-
question_answer2) In Melde's experiment it was found that the string vibrates in 3 loops when 8 gm were placed in the pan. What mass (in gm) must be placed in the pan to make the string vibrate in 5 loops. (Neglect the mass of string)
question_answer3) A transverse wave described by \[y=(0.02m)sin[(1.0\,{{m}^{-1}})x+(30{{s}^{-1}})t]\] Propagates on a stretched string having a linear mass density of\[1.2\times {{10}^{-4}}kg/m\]. Find the tension in the string. (in N)
question_answer4) When a plane wave train transverses a medium, individual particles execute a periodic motion given by the equation \[y=5\sin \frac{\pi }{4}\left( 4t+\frac{x}{16} \right)\]where the lengths are expressed in centimeters and time in seconds. Find the phase difference (in degree) for two positions of the same particles which are occupied at a time interval 0.8 s apart.
question_answer5) In a sonometer wire, the tension is maintained by suspending a 50.7-kg mass from the free end of the wire. The suspended mass has a volume of 0.0075\[{{m}^{3}}\]. The fundamental frequency of the wire is 260 Hz. If the suspended mass is completely submerged in water, find the fundamental frequency (in Hz).
question_answer6) A wire under tension vibrates with a frequency of 450 per second. What would be the fundamental frequency (in cycle/sec) if the wire were half as long, twice as thick and under one-fourth tension.
question_answer7) A stretched string of 1 m length, fixed at both ends, having a mass of\[5\times {{10}^{-4}}kg\] is under a tension of 20 N. It is plucked at a point situated at 25 cm from one end. Find the stretched string would vibrate with a frequency (in Hz).
question_answer8) Two similar wires on a sonometer are tuned to unison. One wire is 25 cm long and is stretched by 100 gram-weight. Find the length (in cm) of the other wire which is stretched by 400 gram-weight.
question_answer9) A heavy string is tied at one end to a movable support and to a light thread at the other end as shown in figure. The thread goes over a fixed pulley and supports a weight to produce a tension. The lowest frequency with which the heavy string resonates is 120 Hz. If the movable support is pushed to the right by 10 cm so that the joint is placed on the pulley, then find the minimum frequency (in Hz) at which the heavy string can resonate.
question_answer10) A transverse wave is travelling along a horizontal string. The first picture shows the shape of the string at an instant of time. This picture is superimposed on a coordinate system to help you make any necessary measurements. The second picture is a graph of the vertical displacement of one point along the string as a function of time. How far (in cm) does this wave travel along the string in one second?
question_answer11) The speed of a transverse wave, going on a wire having a length 50 cm and mass 5.0 g, is 80 m/s. The area of cross-section of the wire is 1.0 \[m{{m}^{2}}\] and its Young?s modulus is\[16\times {{10}^{11}}N/{{m}^{2}}\]. Find the extension of the wire over its natural length. If it is\[a\times {{10}^{-2}}mm\]. Find value of a.
question_answer12) A string of length 40 cm and weighing 10 g is attached to a spring at one end and to a fixed wall at the other end. The spring has a spring constant of 160 N/m and is stretched by 1.0 cm. if a wave pulse is produced on the string near the wall, how much time will it take to reach the spring? If it is\[a\times {{10}^{-2}}\sec \]. Find value of a.
question_answer13) A 40 cm long wire having a mass 3.2 gm and area of cross-section 1 \[m{{m}^{2}}\]is stretched between the supports 40.05 cm apart. In its fundamental mode it vibrate with a frequency 1000/64 Hz. The young's modulus of the wire is\[a\times {{10}^{9}}N/{{m}^{2}}\]. Then value of a is.
question_answer14) A parabolic pulse given by equation\[y(in\text{ }cm)=0.3-0.1{{\left( x-5t \right)}^{2}}\left( y\ge 0 \right)x\] in meter and t in second travelling in a uniform string. The pulse passes through a boundary beyond which its velocity becomes 2.5 m/s. What will be the amplitude of pulse in mm in this medium after transmission.
question_answer15) A uniform string of length L and total mass M is suspended vertically and a transverse pulse is given at the top end of it. At the same moment a body is released from rest and falls freely from the top of the string. At L/a from the bottom the body pass the pulse. Then the value of a is.
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