A metal wire of linear mass density of $9.8\, g/m$ is stretched with a tension of $10 kg$ weight between two rigid supports $1$ metre apart. The wire passes at its middle point between the poles of a permanent magnet, and it vibrates in resonance when carrying an alternating current of frequency $n.$ The frequency $n$ of the alternating source is ..... $Hz$
AIEEE 2003, Medium
Download our app for free and get started
(b) In condition of resonance, frequency of $a.c.$ will be equal to natural frequency of wire
$n = \frac{1}{{2l}}\sqrt {\frac{T}{m}} = \frac{1}{{2 \times 1}}\sqrt {\frac{{10 \times 9.8}}{{9.8 \times {{10}^{ - 3}}}}} = \frac{{100}}{2} = 50$$Hz$
$n = \frac{1}{{2l}}\sqrt {\frac{T}{m}} = \frac{1}{{2 \times 1}}\sqrt {\frac{{10 \times 9.8}}{{9.8 \times {{10}^{ - 3}}}}} = \frac{{100}}{2} = 50$$Hz$
Download our appand get started for free
Experience the future of education. Simply download our apps or reach out to us for more information. Let's shape the future of learning together!No signup needed.*
Similar Questions
- 1A $20 \mathrm{~cm}$ long string, having a mass of $1.0 \mathrm{~g}$, is fixed at both the ends. The tension in the string is $0.5 \mathrm{~N}$. The string is set into vibrations using an external vibrator of frequency $100 \mathrm{~Hz}$. Find the separation (in $cm$) between the successive nodes on the string.View Solution
- 2View SolutionAt nodes in stationary waves
- 3In a plane progressive wave given by $y = 25\cos (2\pi t - \pi x)$, the amplitude and frequency are respectivelyView Solution
- 4Two sources of sound placed close to each other, are emitting progressive waves given byView Solution
$y_1 = 4\,\,sin\,\,600\pi t$ and $y_2 = 5\,\,sin\,\,608\pi t.$An observer located near these two sources of sound will hear
- 5Two interfering waves have the same wavelength, frequency, and amplitude. They are traveling in the same direction but are $90^o$ out of phase. Compared to the individual waves, the resultant wave will have the same.View Solution
- 6The equation of a stationary wave along a stretched string is given by $y = 5\,sin\, \frac{2\pi }{3}x\, cos\, 40\pi t$ where $x$ and $y$ are in $cm$ and $t$ is in $s$. The separation between two adjacent nodes is ..... $cm$View Solution
- 7A man sitting in a moving train hears the whistle of the engine. The frequency of the whistle is $600 Hz$View Solution
- 8The velocity of waves in a string fixed at both ends is $2 m/s$. The string forms standing waves with nodes $5.0 cm$ apart. The frequency of vibration of the string in $Hz$ isView Solution
- 9$A$ steel wire is used to stretch a spring. An oscillating magnetic field drives the steel wire up and down. $A$ standing wave with three antinodes is created when the spring is stretched by $4.0\, cm$. What stretch of the spring produces a standing wave with two antinodes with same frequency ... $cm$ ?View Solution
- 10An observer starts moving with uniform acceleration $'a'$ towards a stationary sound source of frequency $f.$ As the observer approaches the source, the apparent frequency $f'$ heard by the observer varies with time $t$ as:View Solution