A tube 1.20 m long is closed at one end. A stretched wire is places near the open end. The wire is 0.330 m long and has a mass of 9.60 g. It is fixed at both ends and oscillates in its fundamental mode. By resonance, it sets the air column in the tube into oscillation at that column's fundamental frequency Find (a) that frequency and (b) the tension in the wire.
(a) With $$n = 1$$ (for the fundamental mode of vibration) and 343 m/s for the speed of sound, we obtain
$$f = \dfrac{(1) V_{sound}} {4L_{tube}} = \dfrac{343 \space m/s} {4\left (1.20 \space m \right )} = 71.5 \space Hz$$
(b) For the wire we have
$$f' = dfrac{nv_{wire}} {2L_{wire}} = \dfrac{1} {2L_{wire}} \sqrt{\dfrac{\tau} {\mu}}$$
where $$\mu = m_{wire}/L_{wire}$$. Recognizing that
$$f = f'$$ (both the wire and the air in the tube vibrate at the same frequency), we solve this for the tension $$\tau$$.
$$\tau = \left (2L_{wire} f \right )^{2} \left (\dfrac{m_{wire}} {L_{wire}} \right ) = 4f^{2} m_{wire} L_{wire} = 4\left (7105 \space Hz \right )^{2} \left (9.60 \times 10^{-3} \space kg \right ) \left ( 0.330 \space m \right ) = 64.8 \space N$$.
A stationary source emits sound wave of frequency $$500Hz$$. Two observers moving along a line passing through the source detect sound to be of frequencies $$480Hz$$ and $$530Hz$$, Their respective speeds are, in $$ms^{-1}$$ (Given speed of sound$$=300ms)$$
In a resonance tube the first resonance with a tuning fork occurs at $$16$$ cm and second at $$49$$ cm. If the velocity of sound is $$330$$ m/s, the frequency of tuning fork is :
A steel tube of length $$1.00\ m$$ is struck at one end. A person with his ear close to the other end hears the sound of the bow twice, one traveling through the body of the tube and the other the air in the tube. Find the time gap between the two hearings.
In a standing wave pattern in a vibrating air column, nodes are formed at a distance of $$4.0\ cm$$. If the speed of sound in air is $$328\ m\ s^{-1}$$, find the vibration of the air column.
The separation between a node and the next antinode in a vibrating air column $$25\ cm$$. If the speed of sound in air is $$340\ m\ s^{-1}$$, find the frequency of vibration of the air column.
A piezo electric quartz of young's modulus of electricity $$8\times 10^{10}N/m^2$$ and density $$2.65\times 10^{3}kg/m^3$$ is vibrating in resonant condition. The fundamental frequency of vibrating is $$550\ kHz$$. What is thickness of the plate?
A long tube of length $$l=25\ cm$$ and diameter equal to $$2\ cm$$ is taken and at its mouth air is blown as shown in figure. The sound emitted by tube will have all the frequencies of the group: ( velocity of sound $$=330\ m/s$$)
The water level in a vertical glass tube 1.00 m long can be adjusted to any position in the tube. A tuning fork vibrating at 686 Hz is held just over the open top end of the tube, to set up a standing wave of sound in the air-filled top portion of the tube. (That air-filled top portion acts as a tube with one end closed and the other end open.) (a) For how many different positions of the water level will sound from the fork set up resonance in the tube's air-filled portion? What are the (b) least and (c) second least water heights in the tube for resonance to occur?
The frequency of the forks.
One end of the tube is now closed. Calculate the lowest frequency of resonance for the tube.