A wave travelling along a string is described by y=0.005 sin(40 x-2 t) in SI units. The waveleng

step 1 In this question we will learn about some basic concept of the oscillation and waves, right? The

A wave travelling along a string is described by y=0.005...

A wave travelling along a string is described by $\mathrm{y}=0.005 \sin (40 \mathrm{x}-2 \mathrm{t})$ in SI units. The wavelength and frequency of the wave are $\ldots \ldots \ldots$ (A) $(\pi / 5) \mathrm{m} ; 0.12 \mathrm{~Hz}$ (B) $(\pi / 10) \mathrm{m} ; 0.24 \mathrm{~Hz}$ (C) $(\pi / 40) \mathrm{m} ; 0.48 \mathrm{~Hz}$ (D) $(\pi / 20) \mathrm{m} ; 0.32 \mathrm{~Hz}$

A wave travelling along a string is described by $\mathrm{y}=0.005 \sin (40 \mathrm{x}-2 \mathrm{t})$ in SI units. The wavelength and
frequency of the wave are $\ldots \ldots \ldots$
(A) $(\pi / 5) \mathrm{m} ; 0.12 \mathrm{~Hz}$
(B) $(\pi / 10) \mathrm{m} ; 0.24 \mathrm{~Hz}$
(C) $(\pi / 40) \mathrm{m} ; 0.48 \mathrm{~Hz}$
(D) $(\pi / 20) \mathrm{m} ; 0.32 \mathrm{~Hz}$

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Key Concepts

Frequency

Frequency refers to the number of complete cycles that pass a given point per unit time, typically measured in Hertz (Hz). It is derived from the angular frequency and is critical in determining how fast a wave oscillates over time.

Wave Equation

A wave equation mathematically represents a disturbance that propagates through space and time, typically using sinusoidal functions. It encapsulates the behavior of moving waves by combining both spatial and temporal variables to define the amplitude of the oscillation at any point.

Wave Number

The wave number, often denoted by k, describes the number of wave cycles per unit distance and is inversely related to the wavelength. It determines how rapidly the wave oscillates in space and is used to calculate the wavelength using the relation wavelength = 2?/k.

Angular Frequency

Angular frequency, represented by ?, quantifies how fast the wave oscillates in time, measured in radians per second. It is connected to the frequency (in Hertz) by the relationship frequency = ?/(2?), which helps in understanding the temporal aspect of the wave.

Wavelength

Wavelength is the physical distance between consecutive points in phase on a wave, such as peaks or troughs. It can be derived from the wave number and is a key parameter in describing the spatial extent of a single oscillation cycle.

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