Physics, 13.01.2021 15:20 sheilashair

A whistle emitting a note of 4 kHz is whirled in a horizontal circle of radius 1 m at a constant speed. If the highest note heard
by a person a large distance away is 4200 Hz, find:
(i) the speed of the whistle
(ii) the lowest note heard by the person,
(iii) the time taken for the whistle to make on complete revolution,
(iv) the time interval between the person hearing the highest and lowest note.

Answers: 3

Show answers

Answers

Answer from: Alexandragurule18

(i) The speed of the whistle is 16. $\overline 3$ m/s

(ii) The lowest note heard by the person is 3,818. $\overline{18}$ Hz

(iii) The time taken for the whistle to make one revolution is approximately 0.38468 seconds

(iv) The time interval between the person hearing the highest and lowest note is approximately 0.19234 seconds

Explanation:

The question relates to the Doppler effect for which the change in frequency is given as follows;

$f_L = \left ( \dfrac{v \pm v_L }{v \pm v_S} \right ) \cdot f_S$

Where;

f_L = The frequency heard by the listener

v = The speed of sound in air = 343 m/s

v_L = The listener's speed

v_S = The source's (whistle) speed

f_S = The frequency of the source

The given parameters are;

The frequency of the whistle (source), f_S = 4 kHz = 4,000 Hz

The radius of the horizontal circle around which the whistle is whirled = 1 m

The highest note heard by a person a large distance away = 4200 Hz

The distant listener is taken as stationary, v_L = 0 m/s

We therefore have;

$f_L = \left ( \dfrac{v \pm 0 }{v \pm v_S} \right ) \cdot f_S = \left ( \dfrac{v }{v \pm v_S} \right ) \cdot f_S$

(i) When the whistle's motion while it is being whirled towards the listener, v_S is negative

When the whistle's motion while it is being whirled is away from listener, v_S is positive

The highest note, $f_{LH}$ , is obtained with the lowest denominator, that is when the source moves towards the listener and v_S is negative, we get;

$f_{LH} = 4,200 \ Hz = \left ( \dfrac{343 \ m/s }{343 \ m/s - v_S} \right ) \times 4,000 \ Hz$

$\dfrac{4,200 \ Hz}{4,000 \ Hz} = \dfrac{21}{20} = \dfrac{343 \ m/s}{343 \ m/s - v_S}$

21·(343 m/s - v_S ) = 20×343 m/s

21 × v_S = 21 × 343 m/s - 20 × 343 m/s = 343 m/s

v_S = (343 m/s)/21 = 49/3 m/s = 16. $\overline 3$ m/s

The speed of the source = The speed of the whistle

∴ The speed of the source = v_S = 16. $\overline 3$ m/s = The speed of the whistle

(ii) The lowest note heard by the person occurs when the denominator of the formula for the change in frequency is smallest for which we have the value of v_S as positive and the source moves away from the observer which is presented as follows;

$f_{LH} = \left ( \dfrac{343 \ m/s }{343 \ m/s +16.\overline 3 \ m/s } \right ) \times 4,000 \ Hz = 3,818.\overline {18} \ Hz$

The lowest note heard by the person = 3,818. $\overline{18}$ Hz

(iii) The angular velocity of the whistle, ω is given as follows;

$\omega = \dfrac{\theta}{t} = \dfrac{v_S}{r} = \dfrac{16. \overline 3 \ m/s}{1 \ m} = 16. \overline 3 \ radians/second$

The angle rotated in one revolution, is 2·π radians, therefore, when θ = 2·π radians, the time, t_c , to complete one revolution is given as follows;

$t_c = \dfrac{\theta}{\omega} = \dfrac{2 \times \pi \ radians}{16. \overline 3 \ radians/second} \approx 0.385 \ seconds$

Therefore, the time to complete one revolution ≈ 0.38468 seconds

(iv) The time interval between the person hearing the highest and lowest note is the time to complete half a cycle ≈ 0.38468/2 seconds ≈ 0.19234 seconds.

Answer from: Quest

The horse latitudes-high-pressure zones about 30 degrees north and 30 degrees south of the equator.-warm air traveling away from the equator cools and sinks-weather tends to be clear and drythe doldrums-low-pressure near equator-air rises and spreads out toward the poles-rising moist air produces clouds and heavy rainthe westerlies-blow from the west-move from the horse latitudes toward the poles.-bring storms across much of the united statesthe tradewinds-blow from the east-move from the horse latitudes toward the equator -strong, steady winds

Answer from: Quest

the independent variable, or the one that is intentionally manipulated is the speed.

Another question on Physics

Physics, 22.06.2019 10:30

Light from a sodium lamp passes through a diffraction grating that has 1000 slits per millimeter. the interference pattern is viewed on a screen 1.000 m behind the grating. the first (m = 1) two bright yellow fringes that are visible are 0.7288 m and 0.7300 m from the central maximum. what are the wavelengths of these two fringes?

Answers: 2

Answer

Physics, 22.06.2019 18:30

Asmall grinding wheel has a moment of inertia of 4.0×10−5 kg⋅m2 . what net torque must be applied to the wheel for its angular acceleration to be 150 rad/s2 ?

Answers: 3

Answer

Physics, 22.06.2019 22:30

Materials will have different energies associated with the electrons inside them. this is related to how strongly bound they are by their work function. if we sandwich a material with a very low energy between two materials with a high energy, we create a trap for an electron. if this trap is very narrow in one direction in comparison to the others, this is approximately a 1-dimensional box that confines the electron. what is the lowest energy of an electron in the box if the thinnest direction across the materials is 4.81 nm?

Answers: 3

Answer

Physics, 23.06.2019 02:00

Which of the following is the largest disadvantage of about half of the electricity in the united states comes from burning

Answers: 2

Answer

You know the right answer?

A whistle emitting a note of 4 kHz is whirled in a horizontal circle of radius 1 m at a constant sp...

Questions