Calculate the speed of sound in oxygen from the following data.
Question: Calculate the speed of sound in oxygen from the following data. The mass of $22.4$ litre of oxygen at STP ( $T=273 \mathrm{~K}$ and $p=$ $1.0 \times 10^{5} \mathrm{~N} \mathrm{~m}^{-2}$ ) is $32 \mathrm{~g}$, the molar heat capacity of oxygen at constant volume is $C_{\mathrm{V}}=2.5 \mathrm{R}$ and that at constant pressure is $C_{p}=3.5 \mathrm{R}$. Solution:...
Read More →Two point sources of sound are kept at a separation of
Question: Two point sources of sound are kept at a separation of $10 \mathrm{~cm}$. They vibrate in phase to produce waves of wavelength $5.0 \mathrm{~cm}$. What would be the phase difference between the two waves arriving at a point $20 \mathrm{~cm}$ from one source (a) on the line joining the sources and (b) on the perpendicular bisector of the line joining the sources? Solution:...
Read More →A sound wave frequency 100 Hz is travelling in air.
Question: A sound wave frequency $100 \mathrm{~Hz}$ is travelling in air. The speed of sound in air is $350 \mathrm{~m} \mathrm{~s}^{-1}$. (a) By how much is the phase changed at a given point in $2.5 \mathrm{~ms}$ ? (b) What is the phase difference at a given instant between two points separated by a distance of $10.0 \mathrm{~cm}$ along the direction of propagation? Solution:...
Read More →The equation of a travelling sound wave is
Question: The equation of a travelling sound wave is $y=6.0 \sin (600 t-1.8 x)$ where $y$ is measured in $10^{-5} \mathrm{~m}, t$ in second and $x$ in metre. (a) Find the ratio of the displacement amplitude of the particles to the wavelength of the wave. (b) Find the ratio of the velocity amplitude of the particles to the wave speed Solution:...
Read More →Ultrasonic waves of frequency 4.5 MHz are used to
Question: Ultrasonic waves of frequency $4.5 \mathrm{MHz}$ are used to detect tumour in soft tissue. The speed of sound in tissue is $1.5 \mathrm{~km} \mathrm{~s}^{-1}$ and that in air is $340 \mathrm{~m} \mathrm{~s}^{-1}$. Find the wavelength of this ultrasonic wave in air and in tissue. Solution:...
Read More →Find the values of a and b so that the function
Question: Find the values of a and b so that the function $f(x)=\left\{\begin{array}{c}\left(x^{2}+3 x+a\right), \text { when } x \leq 1 ; \\ (b x+2), \text { when } x1\end{array}\right.$ is differentiable at each $x \in R$ Solution:...
Read More →Solve this following
Question: Let $f(x)=\left\{\begin{array}{ll}(2+x), \text { if } x \geq 0 ; \\ (2-x), \text { if } x0\end{array}\right.$ Show that $f(x)$ is not derivable at $x=0$ Solution: Given function $f(x)=\left\{\begin{array}{l}(2+x), \text { if } x \geq 0 \\ (2-x), \text { if } x0\end{array}\right.$...
Read More →Show that function
Question: Show that function $f(x)=\left\{\begin{array}{l}(1-x), \text { when } x1 ; \\ \left(x^{2}-1\right), \text { when } x \geq 1\end{array}\right.$ is continuous but not differentiable at $x=1$ Solution:...
Read More →Solve this following
Question: Show that $f(x)=[x]$ is neither continuous nor derivable at $x=2$. Solution: As, LHD $\neq$ RHD...
Read More →Solve this following
Question: Let $f(x)=\left\{\begin{array}{r}(2-x), \text { when } x \geq 1 \\ x, \text { when } 0 \leq x \leq 1\end{array}\right.$ Show that $f(x)$ is continuous but not differentiable at $x=1$ Solution:...
Read More →Sound waves from a loudspeaker spread nearly uniformly
Question: Sound waves from a loudspeaker spread nearly uniformly in all directions if the wavelength of the sound is much larger than the diameter of the loudspeaker. (a)Calculate the frequency for which the wavelength of sound in air is ten times the diameter of the speaker if the diameter is $20 \mathrm{~cm}$. (b) Sound is essentially transmitted in the forward direction if the wavelength is much shorter than the diameter of the speaker. Calculate the frequency at which the wavelength of the s...
Read More →Solve this following
Question: Show that $f(x)=|x-5|$ is continuous but not differentiable at $x=5$ Solution: $f(x)$ is not differentiable at $x=5$...
Read More →Find the minimum and maximum wavelengths of
Question: Find the minimum and maximum wavelengths of sound in water that is in the audible range ( $20-20000 \mathrm{~Hz})$ for an average human ear. Speed of sound in water $=1450 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →A person can hear sound waves in the frequency range
Question: A person can hear sound waves in the frequency range $20 \mathrm{~Hz}$ to $20 \mathrm{kHz}$. Find the minimum and the maximum wavelengths of sound that is audible to the person. The speed of sound is $360 \mathrm{~m} \mathrm{~s}^{-1}$. Solution:...
Read More →Show that constant function is always differentiable
Question: Show that constant function is always differentiable Solution:...
Read More →A man stands before a large wall at a distance of
Question: A man stands before a large wall at a distance of $50.0 \mathrm{~m}$ and claps his hands at regular intervals. Initially, the interval is large. He gradually reduces the interval and fixes it at a value when the echo of a clap merges every 3 seconds, find the velocity of sound in air. Solution:...
Read More →At a prayer meeting,
Question: At a prayer meeting, the disciples sing JAI-RAM JAI-RAM. The sound amplified by a loudspeaker comes back after reflection from a building at a distance of $80 \mathrm{~m}$ from the meeting. What maximum time interval can be kept between one JAl-RAM and the next JAI-RAM so that the echo does not disturb a listener sitting in the meeting. Speed of sound in air is $320 \mathrm{~m} \mathrm{~s}^{-1}$. Solution: Distance travelled by sound to come back $=80 \times 2=160 \mathrm{~m}$ Time int...
Read More →Solve this following
Question: Show that $f(x)=(x-1)^{1 / 3}$ is not differentiable at $x=1$. Solution:...
Read More →Solve this following
Question: Show that $f(x)=x^{3}$ is continuous as well as differentiable at $x=3$. Solution:...
Read More →A steel tube of length 1.00 m is struck at one end person with
Question: A steel tube of length 1.00 m is struck at one end person with his ear close to the other end hears the sound of the blow twice, one travelling through the body of the tube and the other through the air in the tube. Find the time gap between the two hearings. Use the table in the text for speeds of sound in various substances. Solution:...
Read More →Discus the continuity of the function
Question: Discus the continuity of the function $f(x)=|x|+|x-1|$ in the interval of $[-1,2]$ Solution:...
Read More →A heavy string is tied at one end to a movable support and
Question: A heavy string is tied at one end to a movable support and to a light thread at the other end as shown in the below 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 $120 \mathrm{~Hz}$. If the movable support is pushed to the right by $10 \mathrm{~cm}$ so that the joint is placed on the pulley, what will be the minimum frequency at which the heavy string can resonate? Solution:...
Read More →A 2.00m long rope, having a mass of 80g,
Question: A $2.00 \mathrm{~m}$ long rope, having a mass of $80 \mathrm{~g}$, is fixed at one end and is tied to a light string at the other end. The tension in the string is $256 \mathrm{~N}$ a. Find the frequencies of the fundamental and the first two overtones. b. Find the wavelength in the fundamental and the first overtones. Solution:...
Read More →The figure shows a string stretched by a block going over a pulley.
Question: The figure shows a string stretched by a block going over a pulley. The string vibrates in its tenth harmonic in unison with a particular tuning fork. When a beaker containing water is brought under the block so that the block is completely dipped into the beaker, the string vibrates in its eleventh harmonic. Find the density of the material of the block. Solution:...
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