Question 11:
easyA hospital uses an ultrasonic scanner to locate tumours in a tissue. The operating frequency of the scanner, is $4.2 \text{ MHz}$. The speed of sound in a tissue is $1.7 \text{ km/s}$. The wavelength of sound in the tissue is close to:
(1995)
Wavelength $\lambda = \frac{v}{f} = \frac{1.7 \times 10^3}{4.2 \times 10^6} \approx 4 \times 10^{-4} \text{ m}$.
Question 12:
easyWhich one of the following represents a wave?
(1994)
The equation $y = A \sin(\omega t - kx)$ correctly relates spatial and temporal variations indicating a progressive wave.
Question 13:
moderateA stationary wave is represented by $y = A \sin(100t) \cos(0.01x)$, where $y$ and $A$ are in millimetres, $t$ is in seconds and $x$ is in metres. The velocity of the wave is:
(1994)
For the constituent waves, $\omega = 100$ and $k = 0.01$. Velocity $v = \frac{\omega}{k} = \frac{100}{0.01} = 10^4 \text{ m/s}$.
Question 14:
moderateA wave of frequency $100 \text{ Hz}$ travels along a string towards its fixed end. When this wave travels back, after reflection, a node is formed at a distance of $10 \text{ cm}$ from the fixed end. The speed of the wave (incident and reflected) is:
(1994)
Distance from fixed end (node) to nearest node is $\frac{\lambda}{2} = 10 \text{ cm} = 0.1 \text{ m}$. Thus $\lambda = 0.2 \text{ m}$. Velocity $v = f\lambda = 100 \times 0.2 = 20 \text{ m/s}$.
Question 15:
moderateThe temperature at which the speed of sound becomes double as was at $27^{\circ}\text{C}$ is:
(1993)
Since $v \propto \sqrt{T}$, to double the speed, temperature must be quadrupled. $T_1 = 273 + 27 = 300 \text{ K}$. $T_2 = 4 \times 300 = 1200 \text{ K}$, which is $1200 - 273 = 927^{\circ}\text{C}$.
Question 16:
easyThe frequency of sinusoidal wave $y = 0.40 \cos[2000t + 0.80]$ would be:
(1992)
Comparing with $y = A \cos(\omega t + \phi)$, $\omega = 2000$. Since $\omega = 2\pi f$, $f = \frac{2000}{2\pi} = \frac{1000}{\pi} \text{ Hz}$.
Question 17:
easyWith the propagation of a longitudinal wave through a material medium, the quantities transmitted in the propagation direction are:
(1992)
Mechanical waves transmit energy and linear momentum from one region to another without the transport of matter (mass).
Question 18:
easyVelocity of sound waves in air is $330 \text{ m/s}$. For a particular sound wave in air, a path difference of $40 \text{ cm}$ is equivalent to phase difference of $1.6\pi$. The frequency of this wave is:
(1990)
Phase difference $\Delta\phi = \frac{2\pi}{\lambda} \Delta x \implies 1.6\pi = \frac{2\pi}{\lambda}(0.4) \implies \lambda = \frac{0.8}{1.6} = 0.5 \text{ m}$. Frequency $f = \frac{v}{\lambda} = \frac{330}{0.5} = 660 \text{ Hz}$.
Question 19:
moderateIf the amplitude of sound is doubled and the frequency reduced to one fourth, the intensity of sound at the same point will be:
(1989)
Intensity $I \propto A^2 f^2$. New intensity $I' \propto (2A)^2 (f/4)^2 = 4A^2 \times \frac{f^2}{16} = \frac{1}{4} I$. Thus it decreases by a factor of 4.
Question 20:
moderateThe velocity of sound in any gas depends upon:
(1988)
The velocity of sound in a gaseous medium is determined by the formula $v = \sqrt{\frac{E}{\rho}}$, showing dependence on elasticity ($E$) and density ($\rho$).