question 23 (1 point)\na coil lies flat on a horizontal table top in a region where the magnetic field…

question 23 (1 point)\na coil lies flat on a horizontal table top in a region where the magnetic field points straight down. the magnetic field disappears suddenly. when viewed from above, what is the direction of the induced current in this coil as the field disappears?\n○ counterclockwise\n○ clockwise\n○ clockwise initially, then counterclockwise before stopping\n○ there is no induced current in this coil.

question 23 (1 point)\na coil lies flat on a horizontal table top in a region where the magnetic field points straight down. the magnetic field disappears suddenly. when viewed from above, what is the direction of the induced current in this coil as the field disappears?\n○ counterclockwise\n○ clockwise\n○ clockwise initially, then counterclockwise before stopping\n○ there is no induced current in this coil.

Answer

Explanation:

Step1: Recall the Doppler Effect formula for a moving source

The Doppler Effect formula for a source moving towards a stationary observer is:
( f' = f \cdot \frac{v}{v - v_s} )
where:

  • ( f' ) = observed frequency,
  • ( f ) = source frequency,
  • ( v ) = speed of sound,
  • ( v_s ) = speed of the source (towards the observer, so positive in this context).

Step2: Substitute the given values

We know:

  • ( f = 1000 , \text{Hz} ),
  • ( v_s = \frac{v}{2} ) (source speed is half the speed of sound),
  • ( v ) = speed of sound.

Substitute ( v_s = \frac{v}{2} ) into the formula:
( f' = 1000 \cdot \frac{v}{v - \frac{v}{2}} )

Step3: Simplify the expression

Simplify the denominator:
( v - \frac{v}{2} = \frac{v}{2} )

Now, substitute back:
( f' = 1000 \cdot \frac{v}{\frac{v}{2}} )

The ( v ) terms cancel out:
( f' = 1000 \cdot \frac{1}{\frac{1}{2}} = 1000 \cdot 2 = 2000 , \text{Hz} )? Wait, no—wait, that can’t be right. Wait, no, wait: the formula for a moving source towards a stationary observer is ( f' = f \cdot \frac{v}{v - v_s} ). Wait, if ( v_s = v/2 ), then ( v - v_s = v - v/2 = v/2 ). So ( f' = 1000 \cdot \frac{v}{v/2} = 1000 \cdot 2 = 2000 , \text{Hz} ). But the selected option is 1500 Hz, which is incorrect? Wait, no—wait, maybe I mixed up the formula. Wait, no: the Doppler effect for a moving source: when the source moves towards the observer, the observed frequency is higher. The formula is ( f' = f \cdot \frac{v}{v - v_s} ) (source moving towards observer: ( v_s ) is positive, so denominator is smaller, frequency increases). Wait, but if ( v_s = v/2 ), then ( v - v_s = v/2 ), so ( f' = 1000 \cdot \frac{v}{v/2} = 2000 , \text{Hz} ). But the option selected in the image is 1500 Hz, which is wrong. Wait, maybe the formula is different? Wait, no—let’s check again. Wait, maybe the formula is ( f' = f \cdot \frac{v + v_o}{v - v_s} ), but the observer is stationary, so ( v_o = 0 ). So it’s still ( f' = f \cdot \frac{v}{v - v_s} ). So with ( v_s = v/2 ), ( f' = 1000 \cdot \frac{v}{v - v/2} = 1000 \cdot 2 = 2000 , \text{Hz} ). So the correct answer should be 2000 Hz, not 1500 Hz. Wait, but the image shows 1500 Hz selected, which is incorrect. So the correct answer is 2000 Hz.

Wait, maybe I made a mistake in the formula. Let me confirm: the Doppler effect for sound, when the source is moving towards a stationary observer, the formula is ( f' = f \cdot \frac{v}{v - v_s} ), where ( v ) is the speed of sound, ( v_s ) is the speed of the source towards the observer. Yes, that’s correct. So if ( v_s = v/2 ), then ( f' = 1000 \cdot \frac{v}{v - v/2} = 1000 \cdot 2 = 2000 , \text{Hz} ). So the correct answer is 2000 Hz.

Answer:

A. 2000 Hz