Show that the standard equation y = a sin 2 π λ V t - x of a progressive wave can alternatively be written as y = a sin 2 π n t - x λ .

The standard equation of a progressive wave is y = a sin 2 π λ V t - x where a is the amplitude of the wave, λ is the wavelength of the wave, V is the wave velocity of the wave, t is the time taken and x is the distance from the origin. The equation can also be written as y = a sin 2 π Vt λ - x λ . But we know that, V = n λ where n is the frequency of the wave. So, the above equation can be written as y = a sin 2 π n t - x λ ∵ V λ = n .

Show that the standard equation y = a sin 2 π λ V t - x of a progressive wave can alternatively be written as y = a sin 2 π t T - x λ .

The standard equation of a progressive wave is y = a sin 2 π λ V t - x where a is the amplitude of the wave, λ is the wavelength of the wave, V is the wave velocity of the wave, t is the time taken and x is the distance from the origin. The equation can also be written as y = a sin 2 π Vt λ - x λ . But we know that, V = λ T where T is the time period of the wave. So, the above equation can be written as y = a sin 2 π t T - x λ ∵ V λ = 1 T .

Show that the standard equation y = a sin 2 π λ V t - x of a progressive wave can alternatively be written as y = a sin 2 π n t - x V .

The standard equation of a progressive wave is y = a sin 2 π λ V t - x where a is the amplitude of the wave, λ is the wavelength of the wave, V is the wave velocity of the wave, t is the time taken and x is the distance from the origin. The equation can also be written as y = a sin 2 π V λ t - x V . But we know that, V = n λ where n is the frequency of the wave. So, the above equation can be written as y = a sin 2 π n t - x V ∵ V λ = n .

Show that the standard equation y = a sin 2 π λ V t - x of a progressive wave can alternatively be written as y = a sin ω t - x V .

The standard equation of a progressive wave is y = a sin 2 π λ V t - x where a is the amplitude of the wave, λ is the wavelength of the wave, V is the wave velocity of the wave, t is the time taken and x is the distance from the origin. The equation can also be written as y = a sin 2 π V λ t - x V . But we know that, V = n λ where n is the frequency of the wave. So, the above equation can be written as y = a sin 2 π n t - x V ∵ V λ = n . Now, we know that the angular frequency is given by the relation, ω = 2 π n . Thus, substituting this value of 2 π n in the above equation of progressive wave we get, y = a sin ω t - x V .

What is the relation between the wavelength frequency and wavevelocity

EASY

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 22 - Waves>EXERCISE>Q 2

Show that the standard equation

y = a \sin \frac{2 π}{λ} (V t - x)

of a progressive wave can alternatively be written as

y = a \sin 2 π (n t - \frac{x}{λ})

.

EASY

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 22 - Waves>EXERCISE>Q 2

Show that the standard equation

y = a \sin \frac{2 π}{λ} (V t - x)

of a progressive wave can alternatively be written as

y = a \sin 2 π (\frac{t}{T} - \frac{x}{λ})

.

EASY

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 22 - Waves>EXERCISE>Q 2

Show that the standard equation

y = a \sin \frac{2 π}{λ} (V t - x)

of a progressive wave can alternatively be written as

y = a \sin 2 π n (t - \frac{x}{V})

.

EASY

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 22 - Waves>EXERCISE>Q 2

Show that the standard equation

y = a \sin \frac{2 π}{λ} (V t - x)

of a progressive wave can alternatively be written as

y = a \sin ω (t - \frac{x}{V})

.

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 22 - Waves>EXERCISE>Q 3

A transverse wave is travelling along a string from left to right. The below figure represents the shape of the string at a given instant. $A$ , $B$ , $C$ , $D$ , $E$ , $F$ , $G$ and $H$ are points on the string. At this instant, which of the above points have an upward velocity?

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MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 22 - Waves>EXERCISE>Q 3

A transverse wave is travelling along a string from left to right. The below figure represents the shape of the string at a given instant. $A$ , $B$ , $C$ , $D$ , $E$ , $F$ , $G$ and $H$ are points on the string. At this instant, which of the above points have a downward velocity?

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MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 22 - Waves>EXERCISE>Q 3

A transverse wave is travelling along a string from left to right. The below figure represents the shape of the string at a given instant. $A$ , $B$ , $C$ , $D$ , $E$ , $F$ , $G$ and $H$ are points on the string. At this instant, which of the above points have zero velocity?

Question Image

MEDIUM

11th West Bengal Board

IMPORTANT

A Text Book of PHYSICS PART I : CLASS 11>Chapter 22 - Waves>EXERCISE>Q 3

A transverse wave is travelling along a string from left to right. The below figure represents the shape of the string at a given instant. $A$ , $B$ , $C$ , $D$ , $E$ , $F$ , $G$ and $H$ are points on the string. At this instant, which of the above points have maximum magnitude of velocity?

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What is the relation between the wavelength, frequency and wave-velocity?

Important Questions on Waves

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