Two audio speakers are kept some distance apart and are driven by… - Vidyadip

Question

Two audio speakers are kept some distance apart and are driven by the same amplifier system. A person is sitting at a place 6.0m from one of the speakers and 6.4m from the other. If the sound signal is continuously varied from 500Hz to 5000Hz, what are the frequencies for which there is a destructive interference at the place of the listener? Speed of sound in air = 320m/s.

✓

Answer

The path difference of the two sound waves is given by$\triangle\text{L}=6.4-6.0=0.4\text{m}$
The wavelength of either wave = $\lambda=\frac{\text{V}}{\rho}=\frac{320}{\rho}(\text{m/s})$ For destructive interference $\triangle\text{L}=\frac{(2\text{n}+1)\lambda}{2}$ where n is an integers. Or $0.4\text{m}=\frac{2\text{n}+1}{2}\times\frac{320}{\rho}$$\Rightarrow\rho=\text{n}=\frac{320}{0.4}=800\frac{2\text{n}+1}{2}\text{Hz}=(2\text{n}+1)400\text{Hz}$
Thus the frequency within the specified range which cause destructive interference are 1200Hz, 2000Hz, 2800Hz, 3600Hz and 4400Hz.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "5 Marks Questions" from Sound Waves→Sound Waves — all question types→Physics STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

The radii of curvature of a lens are +20cm and +30cm. The material of the lens has a refracting index 1.6. Find the focal length of the lens.

If it is placed in air.
If it is placed in water $(\mu=1.33).$

A bicycle is resting on its stand in the east$-$west direction and the rear wheel is rotated at an angular speed of $100$ revolutions per minute. If the length of each spoke is $30.0\ cm$ and the horizontal component of the earth's magnetic field is $2.0 \times 10^{-5} T,$ find the emf induced between the axis and the outer end of a spoke. Neglect centripetal force acting on the free electrons of the spoke.

Suppose that the electric field amplitude of an electromagnetic wave is $E_0 = 120 N/C$ and that its frequency is $ν = 50.0 MHz. (a)$ Determine $, B_0, ω, k,$ and $\lambda . (b)$ Find expressions for $E$ and $B$.

Calculate potential energy of a point charge -q placed along the axis due to a charge +Q uniformly distributed along a ring of radius R. Sketch P.E. as a function of axial distance z from the centre of the ring. Looking at graph, can you see what would happen if -q is displaced slightly from the centre of the ring (along the axis)?

Explain quantitatively the order of magnitude difference between the diamagnetic susceptibility of $N_2 (~5 \times 10^{-9}) \ ($at $\text{STP})$ and $Cu (~10^{-5}).$

Find the value of $\frac{\text{i}_1}{\text{i}_2}$ in the figure. if (a) $\text{R}=0.1\Omega$ (b) $\text{R}=1\Omega$ and (c) $\text{R}=10\Omega.$ Note from your answers that in order to get more current from a combination of two batteries, they should be joined in parallel if the external resistance is small and in series if the external resistance is large, compared to the internal resistance.

State Biot-Savart statement. Obtain an expression for produced magnetic field due to a straight and limited length of current carrying conductor wire. Write its similarities and differences with coulomb's law of electrostatics.

Compare three magnetic substances on the basis of following properties :
(i) Behaviour in magnetic field
(ii) Main reason for magnet formation
(iii) Behaviour in non-uniform magnetic field
(iv) Behaviour on bringing magnetic pole near
(v) Magnitude of $\mu_r$
(vi) Number of field lines passing through substance in magnetic field
(vii) Direction of magnetisation.

A vessel of volume $125\ cm^3$ contains tritium $\big(\text{ }^3\text{H,t}_{\frac{1}{2}}=12.3\text{y}\big)$ at $500\ \text{kPa}$ and $300K$. Calculate the activity of the gas.

Figure. shows the variation in the internal energy $U$ with the volume $V$ of $2.0\ mol$ of an ideal gas in a cyclic process abcda. The temperatures of the gas at $b$ and $c$ are $500K$ and $300K$ respectively. Calculate the heat absorbed by the gas during the process.