Consumer electrical power in the America's is typically 110V 60Hz. Consumer electrical power in Europe and Southeast Asia is typically 220V 50Hz. Consumer electronics and appliances are designed for use on a specific voltage and frequency or a specific voltage and frequency range.
Many, if not most, low power electronic devices manufactured today incorporate switching power supply technology which allows for use on a wide range of electrical powers. This will Be identified on the nameplate data as: 100-240V 50/60 Hz. All electrical equipments should identify the required electrical power specifications. For safety reasons, both personal and property, you cannot operate the electrical equipment outside the manufacturers required electrical power specifications without risk of physical injury, fire, and/or damage/destruction of the equipment.
When you do not know if your electrical equipment will operate on the utility power available you should call the equipment manufacturer and speak to an applications engineer. It is better to be safe than sorry.
2:1 Step Up/Step Down Transformers will change the voltage by a factor of two. Either 110V in and 220V out or conversely 220V in and 110V out. These transformers do NOT change the frequency. 50 Hertz in will be 50 Hertz out. 60 Hertz in will be 60 Hertz out, regardless of the change in the voltage potential.
50/60 Hertz is very important in equipment that have fans and motors. Fans and motors convert electrical energy to mechanical energy. Energy conversion always has losses. The more efficient the conversion, the cheaper the fan or motor will be to run. When designed and manufactured a motor is tuned to maximize the energy conversion. This will be for the expected electrical power frequency of operation, be it 50 or 60 Hertz. If the unit is operated on the wrong frequency, it may run sluggishly, run inefficiently, be damaged or destroyed and may possibly catch fire.